Mail from "all inboxes" clearing themselves

So i received a replacement iphone 4 from Verizon. Did the whole back up and stuff from my old phone through itunes. Well now my mail ( hotmail, gmail) are collected in the all inboxes. 10-15 later it clears/moves themselves to each individual boxes and is no longer in the all inboxes folder. The problem is, if i dont catch the email before they move i wont know i got them unless i go into individual boxes and check each and every one.